2. The Miss Manners Renery in Dry Rock, Oklahoma, converts crude oil into gasoline. It takes 1 barrel of crude oil to produce 1 barrel of gasoline. In addition to the cost of oil there are some other costs involved in rening gasoline. Total costs of producing y barrels of gasoline are described by the cost function C(y) = y2 / 2 + pay, where pa is the price of a barrel of crude oil. (a) Express the marginal cost of producing gasoline as a function of pa and y. (b) Suppose that the renery can buy 50 barrels of crude oil for $5 a barrel but must pay $15 a barrel for any more that it buys beyond 50 barrels. What is the marginal cost curve for gasoline? (c) Plot Miss Manners\" supply curve. ((1) Suppose that Miss Manners faces a horizontal demand curve for gasoline at a price of $30 per barrel. Plot this demand curve on the graph above. How much gasoline will she supply? (e) If Miss Manners could no longer get the rst 50 barrels of crude for $5, but had to pay $15 a barrel for all crude oil, how would her output change? (f) Now suppose that an entitlement program is introduced that permits reneries to buy one barrel of oil at $5 for each barrel of oil that they buy for $15. What will Miss Manners' supply curve be now? Assume that it can buy fractions of a barrel in the same manner. Plot this supply curve on the graph above. If the demand curve is horizontal at $30 a barrel, how much gasoline will Miss Manners supply now